As a simple example of the convolutional approach, we can consider the problem of noise removal from a digitised image. In the case of an electro-optical system noise may be present due to electrical sensor noise or due to post-sensor amplification, A/D conversion etc. If image noise arises from a noisy sensor or channel transmission errors, it will appear as spatially uncorrelated high-frequency components, i.e. random light and dark spots on the image data. Simple low pass filtering may be effective in removing these isolated noise points; the multiplication of the image frequency spectrum by a low-pass filter is equivalent to convolving the original image with the Fourier transform of the low-pass filter. Several possible space-domain masks of low pass form are given below

These noise cleaning masks are normalised to unit magnitude so that the process does not introduce a brightness bias in the processed image. The process of smoothing a noisy image by convolution is illustrated in Figure 8: Convolution Filtering. ( This is not a recommended technique; even a simple median filter is better since the blurring is not so pronounced).

Discrete convolution may also be employed for edge detection, in which case it is possible to use a crude approximation of the Laplacian,

These masks possess the property that the sum of their elements is zero, so that no response is gained from a uniform background or other image area. The Laplacian operator gives edge magnitude only, it is invariant to rotation. The effect of the first of these masks is illustrated in Figure 8, above. (This has been postprocessed by histogram equalisation). The result of the convolution illustrates two primary effects; firstly it tends to increase the slope of the edge transition and secondly it produces overshoot or ringing at either side of the edge. Like the example of smoothing, this is not a good way to detect edges; we consider more appropriate edge detection methods using convolutional operators in the next section.